1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License, Version 1.0 only
6 * (the "License").  You may not use this file except in compliance
7 * with the License.
8 *
9 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
10 * or http://www.opensolaris.org/os/licensing.
11 * See the License for the specific language governing permissions
12 * and limitations under the License.
13 *
14 * When distributing Covered Code, include this CDDL HEADER in each
15 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
16 * If applicable, add the following below this CDDL HEADER, with the
17 * fields enclosed by brackets "[]" replaced with your own identifying
18 * information: Portions Copyright [yyyy] [name of copyright owner]
19 *
20 * CDDL HEADER END
21 */
22/*
23 * Copyright 2004 Sun Microsystems, Inc.  All rights reserved.
24 * Use is subject to license terms.
25 */
26
27#pragma ident	"%Z%%M%	%I%	%E% SMI"
28
29/*
30 * _X_cplx_div(z, w) returns z / w with infinities handled according
31 * to C99.
32 *
33 * If z and w are both finite and w is nonzero, _X_cplx_div delivers
34 * the complex quotient q according to the usual formula: let a =
35 * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
36 * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
37 * r = c * c + d * d.  This implementation scales to avoid premature
38 * underflow or overflow.
39 *
40 * If z is neither NaN nor zero and w is zero, or if z is infinite
41 * and w is finite and nonzero, _X_cplx_div delivers an infinite
42 * result.  If z is finite and w is infinite, _X_cplx_div delivers
43 * a zero result.
44 *
45 * If z and w are both zero or both infinite, or if either z or w is
46 * a complex NaN, _X_cplx_div delivers NaN + I * NaN.  C99 doesn't
47 * specify these cases.
48 *
49 * This implementation can raise spurious underflow, overflow, in-
50 * valid operation, inexact, and division-by-zero exceptions.  C99
51 * allows this.
52 */
53
54#if !defined(i386) && !defined(__i386) && !defined(__amd64)
55#error This code is for x86 only
56#endif
57
58static union {
59	int	i;
60	float	f;
61} inf = {
62	0x7f800000
63};
64
65/*
66 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
67 */
68static int
69testinfl(long double x)
70{
71	union {
72		int		i[3];
73		long double	e;
74	} xx;
75
76	xx.e = x;
77	if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
78		return (0);
79	return (1 | ((xx.i[2] << 16) >> 31));
80}
81
82long double _Complex
83_X_cplx_div(long double _Complex z, long double _Complex w)
84{
85	long double _Complex	v;
86	union {
87		int		i[3];
88		long double	e;
89	} aa, bb, cc, dd, ss;
90	long double	a, b, c, d, r;
91	int		ea, eb, ec, ed, ez, ew, es, i, j;
92
93	/*
94	 * The following is equivalent to
95	 *
96	 *  a = creall(*z); b = cimagl(*z);
97	 *  c = creall(*w); d = cimagl(*w);
98	 */
99	a = ((long double *)&z)[0];
100	b = ((long double *)&z)[1];
101	c = ((long double *)&w)[0];
102	d = ((long double *)&w)[1];
103
104	/* extract exponents to estimate |z| and |w| */
105	aa.e = a;
106	bb.e = b;
107	ea = aa.i[2] & 0x7fff;
108	eb = bb.i[2] & 0x7fff;
109	ez = (ea > eb)? ea : eb;
110
111	cc.e = c;
112	dd.e = d;
113	ec = cc.i[2] & 0x7fff;
114	ed = dd.i[2] & 0x7fff;
115	ew = (ec > ed)? ec : ed;
116
117	/* check for special cases */
118	if (ew >= 0x7fff) { /* w is inf or nan */
119		r = 0.0f;
120		i = testinfl(c);
121		j = testinfl(d);
122		if (i | j) { /* w is infinite */
123			/*
124			 * "factor out" infinity, being careful to preserve
125			 * signs of finite values
126			 */
127			c = i? i : (((cc.i[2] << 16) < 0)? -0.0f : 0.0f);
128			d = j? j : (((dd.i[2] << 16) < 0)? -0.0f : 0.0f);
129			if (ez >= 0x7ffe) {
130				/* scale to avoid overflow below */
131				c *= 0.5f;
132				d *= 0.5f;
133			}
134		}
135		((long double *)&v)[0] = (a * c + b * d) * r;
136		((long double *)&v)[1] = (b * c - a * d) * r;
137		return (v);
138	}
139
140	if (ew == 0 && (cc.i[1] | cc.i[0] | dd.i[1] | dd.i[0]) == 0) {
141		/* w is zero; multiply z by 1/Re(w) - I * Im(w) */
142		c = 1.0f / c;
143		i = testinfl(a);
144		j = testinfl(b);
145		if (i | j) { /* z is infinite */
146			a = i;
147			b = j;
148		}
149		((long double *)&v)[0] = a * c + b * d;
150		((long double *)&v)[1] = b * c - a * d;
151		return (v);
152	}
153
154	if (ez >= 0x7fff) { /* z is inf or nan */
155		i = testinfl(a);
156		j = testinfl(b);
157		if (i | j) { /* z is infinite */
158			a = i;
159			b = j;
160			r = inf.f;
161		}
162		((long double *)&v)[0] = a * c + b * d;
163		((long double *)&v)[1] = b * c - a * d;
164		return (v);
165	}
166
167	/*
168	 * Scale c and d to compute 1/|w|^2 and the real and imaginary
169	 * parts of the quotient.
170	 */
171	es = ((ew >> 2) - ew) + 0x6ffd;
172	if (ez < 0x0086) { /* |z| < 2^-16249 */
173		if (((ew - 0x3efe) | (0x4083 - ew)) >= 0)
174			es = ((0x4083 - ew) >> 1) + 0x3fff;
175	}
176	ss.i[2] = es;
177	ss.i[1] = 0x80000000;
178	ss.i[0] = 0;
179
180	c *= ss.e;
181	d *= ss.e;
182	r = 1.0f / (c * c + d * d);
183
184	c *= ss.e;
185	d *= ss.e;
186
187	((long double *)&v)[0] = (a * c + b * d) * r;
188	((long double *)&v)[1] = (b * c - a * d) * r;
189	return (v);
190}
191